Unfortunately, the answer to this question has to be fairly broad and vague. The plane crashes into a lake somewhere in the Canadian wilderness. Readers are not told the exact heading of the aircraft other than a vague "northwest," but the plane is likely to have crashed in either Quebec or Ontario. New Brunswick is also a possibility but not likely based on the initial heading; however, readers do know that Brian veered off course.
If I had to pick one, I would favor Quebec simply because there are more large lakes in Quebec than Ontario. The reason that the Canadian provinces are the most likely crash-points is because of the plane's departure point. The plane left from a small airport in Hampton, New York which is right on the border of Vermont.
This is where things get tricky to figure out, because Paulsen didn't give readers accurate information regarding the airplane. The second sentence of the story tells readers that the plane is a Cessna 406. A paragraph or so later, the text tells readers that Brian had never been in a single-engine aircraft before. The Cessna 406 is a twin-engine aircraft. The Cessna 406 is called the Caravan II. The Caravan I (Cessna 208) is a single engine variant.
Both aircrafts have a range of about 1,200 miles, and that could put Brian all the way into Manitoba (because he ran the aircraft until it was out of fuel). The problem is that readers are told that the plane's cruising speed was 160 miles per hour. Both the 208 and 406 have cruising speeds well over 200 miles per hour:
Many hours, at maybe 160 miles an hour. Even if it was only a little off course, with that speed and time Brian might now be sitting several hundred miles off to the side of the recorded flight plan.
The plane that fits the description in the book is the Cessna 206. It's a common bush plane and/or float plane because it is quite rugged. It's cruising speed, according to specifications, is 163 miles per hour. It has a range of almost 850 miles, and that easily puts Brian deep into either Quebec or Ontario by the time the fuel ran out.